Optimum interfaces that maximize the heat transfer rate between two conforming conductive media

Shape optimization of conductive-media interfaces using an IGA-BEM solver

“…For a wavy, periodic interface with zero mean, the results are similar to those of a single slab; there is an enhancement of the heat flux, which depends on the geometry of the interface, and for small amplitude corrugations the enhancement is proportional to the square of the amplitude of the corrugations [3]. An isoperimetric optimization algorithm developed by Fyrillas, Leontiou, & Kostas [9] revealed that there is an optimum periodic geometry that maximizes the heat flux.…”

“…In the above references [4,9], besides optimum corrugations, the authors also consider the optimal design of high conductivity inserts, and the optimal design of fins. The optimization problems considered are shape optimization problems and fall into the general area of inverse problems.…”

“…For example, the objective function can be the difference between the computed temperature and the measured/prescribed temperature and the unknowns can be the boundary conditions, physical properties or the geometry of the configuration [10,11,12,13,14,15]. Another example is to have the heat flux as the objective function and obtain the shapes that optimize it [16,17,18,19,20,21,9].…”

“…adaptive mesh [24], eigenfunction expansion [10], and mesh-morphing [25]. Recently, a method that proved effective is to use the boundary element method and define the variables of the optimization as the angles between adjacent elements [9].…”

“…In addition, accuracy is very significant due to the sensitivity of the solution on the parameters of the optimization. Hence, where applicable, the boundary element method [29,30,31] provides a natural selection for the numerical solution of the PDE due to its superiority of handling, with high accuracy, a large number of elements and intricate wall geometries [16,17,18,4,19,20,21,9].…”